Properties

Label 14400.q
Number of curves $2$
Conductor $14400$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14400.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14400.q1 14400s2 \([0, 0, 0, -11340, -464400]\) \(1000188\) \(161243136000\) \([2]\) \(24576\) \(1.0699\)  
14400.q2 14400s1 \([0, 0, 0, -540, -10800]\) \(-432\) \(-40310784000\) \([2]\) \(12288\) \(0.72338\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 14400.q have rank \(0\).

Complex multiplication

The elliptic curves in class 14400.q do not have complex multiplication.

Modular form 14400.2.a.q

sage: E.q_eigenform(10)
 
\(q - 4q^{7} + 4q^{11} - 4q^{13} + 6q^{17} + 4q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.